The actual dragonball anime series
(including the original, Z, and GT) is a lengthy one indeed.
In Japan it took several years, running through most of the 1990's
to air fully and is currently doing such in the USA and other
parts of the world now.

The anime series itself was developed
from the manga itself. Dragonball was a manga series first before
a tv series. The series focuses on Goku from boyhood to adulthood
and even to final death (he dies several times but there IS a
final death in GT). DBZ was originally supposed to feature his
son, Gohan, but when Japanese fans clamored for more Goku, he
was brought back from the dead to take the spotlight once again
and steal the thunder from his son (much to the dismay of Gohan
fans). Many die-hard Dragonball fans denounce DBGT as part of
the series due to Toriyama's lack of input into the series. Truth
is, Toriyama did do the approvals of character designs,etc. for
this series eventhough he didn't work directly on this series.
While short and somewhat rushed, DBGT is still a part of the
Dragonball series regardless of what fans say. It was licensed,etc.
along with the others.

The breakdown of episode counts
(not including movies or tv specials) by saga are as follows
(Japanese count, NOT Americanized version count):

Original Dragonball = 153 episodes

Dragonball Z= 291 episodes

Dragonball GT= 64 episodes

total episodes for series =
508

I will eventually place here
the titles of every episode and perhaps a summary of some.